It has long been proposed to target the delivery of a substance within the body by associating the substance with magnetically responsive carriers (for example magnetite particles) and using magnetic fields and/or gradients to control the carriers, and thus the delivery of the substance. For example, it has been proposed to deliver an antitumor medication to a tumor by coating magnetite particles with the substance, introducing the particles into the patient's blood stream, and guiding the coated magnetite particles to the tumor site with a magnet.
However this method of delivery has been difficult to achieve in practice with very small particles. This is possibly due to the fact that the fluid forces on small particles are much higher than the magnetic forces that can be practically applied to such particles. According to Stokes law the fluid forces on a particle re give byFR=6πvηrwhere: η=viscosity
v=velocity
r=radius
The magnetic forces are:FM=m dB/dz=MVdB/dZ=M(4/3)πr3dB/dZwhere m is the particle magnetic moment, M its magnetization, V its volume, and dB/dZ is the applied magnetic gradient.Setting the fluid forces equal to the magnetic forces:FR=FM6πvηr=M4/3πr3dB/dZdB/dZ=9/2 vη/Mr2
This gives the gradient needed to control a single particle of radius r, magnetization M, in a stream of velocity v, with viscosity η. If η=0.04 poise (for blood), and stream velocity is 100 cm/sec, M=450 emu/cm3, and r=2×10−4 cm, a gradient of 4×106 oersted/cm or 400 T/m is needed to hold the particle in the stream. This magnetization is for pure magnetite. Typical particles might be 10 percent magnetite by volume, so another factor of 10 would be needed for the gradient.
Thus, the magnetic control of small magnetic carrier particles in the bloodstream is difficult, requiring impracticably large gradients.